ICN is one of the few simple triatomic molecules whose photodissociation mechanisms have been thoroughly investigated. Since it has a linear structure in the electronic ground state, the dissociation follows a photoexcitation at a linear or slightly bent structure. It is generally believed that the Ã-band consists of the dominant excitation to 3Π0+ (4A') with the transition dipole moment (TDM) parallel to the molecular axis ( z), a slightly weaker transition to 1Π1 (5A', 4A″), and a much weaker transition to 3Π1 (3A', 2A″), both of the latter two having perpendicular TDMs. In the present work, we have theoretically studied the geometry dependence of these TDMs and found a pronounced θ (bending angle) dependence in the parallel ( z) component of the TDMs to 1Π1 (5A') and 3Π1 (3A'), both of which should be zero at a linear geometry by symmetry and thus have been previously ignored. We estimated that the z component TDM to 1Π1 (5A') has a contribution of 15-20% to the total absorption cross-section at 249 nm at room temperature. Interestingly, the TDM to 3Π0+ (4A') does not exhibit such θ dependency and thus has only the z component. We compare the TDMs of ICN and CH3I molecules having similar excited states. The fact that all the TDMs to 3A', 4A', and 5A' have nonnegligible z components implies the importance of the coherent excitation contributions to various observables of CN fragment, such as the anisotropy parameter, the orientation parameter, and the rotational level distribution as well as the rotational fine structure level distribution.